[1]} and [2]} used a similar graph for N-ary cross-sentence relation extraction. Rather than using explicit paths, they used an LSTM on a graph. A graph LSTM is a general structure for a linear LSTM or tree LSTM. If the graph contains only the word adjacency edges, then the graph LSTM becomes a linear LSTM. If the graph contains the edges from the dependency tree, it becomes a tree LSTM. A general graph structure may contain cycles. So [1]} divides this graph into two directed acyclic graphs (DAG), where the forward DAG contains only the forward edges among the tokens and the backward DAG contains only the backward edges among the tokens. Each node has a separate forget gate for each of its neighbors. It receives information from the neighbors and updates its hidden states using LSTM equations [4]}. If we only consider the word adjacency edges, this graph LSTM becomes a bi-directional linear LSTM. [2]} did not divide the graph into two DAGs, but directly used the graph structure to update the states of the nodes. At time step \(t\) , each node receives information from its neighbor from the previous time step and update its hidden states using LSTM equations. This process is repeated \(k\)  number of times where \(k\)  is a hyper-parameter.
